View source: R/family.extremes.R

cens.gumbel | R Documentation |

Maximum likelihood estimation of the 2-parameter Gumbel distribution when there are censored observations. A matrix response is not allowed.

cens.gumbel(llocation = "identitylink", lscale = "loglink", iscale = NULL, mean = TRUE, percentiles = NULL, zero = "scale")

`llocation, lscale` |
Character.
Parameter link functions for the location and
(positive) |

`iscale` |
Numeric and positive.
Initial value for |

`mean` |
Logical. Return the mean? If |

`percentiles` |
Numeric with values between 0 and 100.
If |

`zero` |
An integer-valued vector specifying which linear/additive predictors
are modelled as intercepts only. The value (possibly values) must be
from the set {1,2} corresponding respectively to |

This VGAM family function is like `gumbel`

but handles observations
that are left-censored (so that the true value would be less than
the observed value) else right-censored (so that the true value would be
greater than the observed value). To indicate which type of censoring,
input `extra = list(leftcensored = vec1, rightcensored = vec2)`

where `vec1`

and `vec2`

are logical vectors the same length
as the response.
If the two components of this list are missing then the logical
values are taken to be `FALSE`

. The fitted object has these two
components stored in the `extra`

slot.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions such as `vglm`

and `vgam`

.

Numerical problems may occur if the amount of censoring is excessive.

See `gumbel`

for details about the Gumbel distribution.
The initial values are based on assuming all uncensored observations,
therefore could be improved upon.

T. W. Yee

Coles, S. (2001).
*An Introduction to Statistical Modeling of Extreme Values*.
London: Springer-Verlag.

`gumbel`

,
`gumbelff`

,
`rgumbel`

,
`guplot`

,
`gev`

,
`venice`

.

# Example 1 ystar <- venice[["r1"]] # Use the first order statistic as the response nn <- length(ystar) L <- runif(nn, 100, 104) # Lower censoring points U <- runif(nn, 130, 135) # Upper censoring points y <- pmax(L, ystar) # Left censored y <- pmin(U, y) # Right censored extra <- list(leftcensored = ystar < L, rightcensored = ystar > U) fit <- vglm(y ~ scale(year), data = venice, trace = TRUE, extra = extra, fam = cens.gumbel(mean = FALSE, perc = c(5, 25, 50, 75, 95))) coef(fit, matrix = TRUE) head(fitted(fit)) fit@extra # Example 2: simulated data nn <- 1000 ystar <- rgumbel(nn, loc = 1, scale = exp(0.5)) # The uncensored data L <- runif(nn, -1, 1) # Lower censoring points U <- runif(nn, 2, 5) # Upper censoring points y <- pmax(L, ystar) # Left censored y <- pmin(U, y) # Right censored ## Not run: par(mfrow = c(1, 2)); hist(ystar); hist(y); extra <- list(leftcensored = ystar < L, rightcensored = ystar > U) fit <- vglm(y ~ 1, trace = TRUE, extra = extra, fam = cens.gumbel) coef(fit, matrix = TRUE)

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